- Determine the ODEs describing the system (PDEs also workable).
- Express all physical quantities (such as force and velocity) in terms of traveling-wave components. The traveling wave components are called wave variables. For example, the force on a mass is decomposed as , where is regarded as a traveling wave propagating toward the mass, while is seen as the traveling component propagating away from the mass. A ``traveling wave'' view of force mediation (at the speed of light) is actually much closer to underlying physical reality than any instantaneous model.
- Next, digitize the resulting traveling-wave system using the bilinear transform (§7.3.2,[449, p. 386]). The bilinear transform is equivalent in the time domain to the trapezoidal rule for numerical integration (§7.3.2).
- Connect elementary units together by means of -port scattering junctions. There are two basic types of scattering junction, one for parallel, and one for series connection. The theory of scattering junctions is introduced in the digital waveguide context (§C.8).
Digital Waveguide Modeling Elements